Carleman embedding turns nonlinear semigroups into linear ones whose convergence follows from dissipativity and Trotter-Kato approximation, even for unbounded generators and as 1-integrated semigroups.
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Optimal control theory is applied to the coagulation-fragmentation equation, establishing existence, stability via Gamma-convergence, optimality conditions, and numerical evidence that a scalar control can reshape particle size distributions.
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Nonlinear semigroups with unbounded generators under Carleman linearization
Carleman embedding turns nonlinear semigroups into linear ones whose convergence follows from dissipativity and Trotter-Kato approximation, even for unbounded generators and as 1-integrated semigroups.
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Optimal control of the coagulation-fragmentation equation
Optimal control theory is applied to the coagulation-fragmentation equation, establishing existence, stability via Gamma-convergence, optimality conditions, and numerical evidence that a scalar control can reshape particle size distributions.